1. Introduction
Bearing is one of the essential parts of rotating machinery, and its damage causes serious failures of rotating machinery and incalculable consequences. Therefore, the bearing fault diagnosis research has become a hot spot. However, in actual working conditions, the fault signals of rotating machinery are difficult to accurately identify due to the complexity of the working condition and the influence of noise signals.
At present, A series of time-frequency analysis methods are proposed to solve these problems, for example, short-time Fourier transform (STFT) [
1], continuous wavelet transform (CWT) [
2], s-transform (ST) [
3] and so on. The essence of time-frequency the analysis is to transform a one-dimensional time-domain signal into two-dimensional time-frequency image to reflect the variation rule of each frequency component of signal with time. Many scholars have applied it to the study of fault diagnosis. Ma et al. [
4] presented a condition monitoring method based on a deep belief network (DBN) optimized by multi-order fractional Fourier transform (FRFT) and sparrow search algorithm (SSA). Firstly, they used fractional Fourier transform based on curve feature segmentation to filter fault vibration signals and extract fault characteristic frequencies. Then, the fault features are input into SSA-DBN model for training and the bearing fault features are classified, recognized and diagnosed. Zhu et al. [
5] extracted the time-frequency characteristics of bearing signals through wavelet packet transform (WPT) and formed the time-frequency characteristic matrix of the signals. Secondly, multi-weight singular value decomposition (MWSVD) was constructed using singular value contribution rate and entropy weight to extract further the characteristics of the time-frequency characteristic matrix obtained by WPT. Finally, the extracted feature matrix is used as the input of the support vector machine (SVM) classifier for bearing fault diagnosis. Gituku et al. [
6] used refined composite multiscale fuzzy entropy (RCMFE) for cross-domain diagnosis of bearing faults and used self-organizing fuzzy (SOF) classifier for classification. Although these methods are easy to implement, the limitations of Heisenberg’s uncertainty principle [
7] prevent them from improving time and frequency resolution. To obtain time-frequency images of vibration signals with better energy concentration, Daubechies et al. [
8] suggested the synchronous squeeze wavelet transform (SSWT). In essence, it is a time-frequency analysis method of energy rearrangement. Based on CWT, spectral energy is redistributed and concentrated at instantaneous frequencies [
9]. Based on this idea, Huang et al. [
10] proposed the synchrosqueezing S transform (SSST). Yu et al. proposed the Multisynchrosqueezing Transform (MSST) [
11] and Time-reassigned Multisynchrosqueezing transform (TMSST) [
12]. They performed multiple iterations based on synchronous compression transformation. They proved that the error between the time-frequency representation obtained and the ideal case becomes smaller with the increase of iterations. In other words, this method can theoretically approach the ideal time-frequency representation infinitely, which makes it widely used in the field of bearing fault diagnosis [
13,
14,
15,
16,
17,
18].
With the development of artificial intelligence, many scholars inducted deep learning into fault diagnosis.In bearing fault diagnosis, Major deep learning networks include autoencoder [
19,
20,
21,
22,
23], Convolutional Neural Networks (CNN), generative adversarial network [
24,
25,
26], Recurrent Neural Networks (RNN) and deep transfer learning [
27,
28,
29].
Considering the characteristics of CNN and RNN, more and more scholars have applied them to rolling bearing fault diagnosis. The original one-dimensional vibration signal was collected as input and feature information was extracted adaptively through CNN [
30,
31,
32,
33]. However, Khorram et al. [
34] combined CNN with short and long duration memory network and proposed a new convolutional short and long duration memory recurrent neural network. In addition, on that basis, some scholars generated the spectrum graph of vibration data through a time-frequency analysis and proposed a lightweight convolutional neural network to classify bearing faults [
35,
36]. Shenfield and Howarth [
37] combined CNN and RNN. They proposed a dual-channel circulating neural network, which solved the problems of domain adaptive and high-frequency noise under actual working conditions. In addition, CNN was also used to extract the features of CWT, STFT and HHT time-frequency images, respectively [
38,
39,
40]. These deep learning methods were novel, but they required more computing resources. Many hyperparameters need to be determined in advance, such as activation function, iteration number, learning rate, convolution kernel size, network layer number, etc.
In summary, in the intelligent fault diagnosis of rolling bearings, many scholars only used one of the methods of frequency compression and time compression. Still, they ignored the different applicable characteristics of the two kinds of methods. The compression along the frequency axis is suitable for signal components with slowly varying frequency (SCSVF). Conversely, compression along the time axis is more suitable for signal components with rapidly varying frequency (SCRVF). Rolling bearing vibration signals collected by sensors are rich and complex, often interwoven with SCSVF and SCRVF. Therefore, the combination of MSST and TMSST can be more conducive to bearing fault diagnosis. In addition, diagnostic models are divided into traditional machine learning models and deep learning models, both of which have advantages and disadvantages. The conventional method is interpreted well, but the process is complicated and has a poor-fitting ability. Deep learning automatically extracts features, but it has a high computational cost and many hyperparameters. Both methods are favored by a large number of researchers. However, the biggest obstacle to their wide application in the field of rolling bearing fault diagnosis is still how to establish a high-precision, and high-efficiency fault diagnosis model [
41,
42]. Therefore, it is crucial to integrate the information of multiple time-frequency images and diagnostic design models with more vital feature extraction ability and better performance. Meanwhile, the above methods have great advantages in the case of constant speed, but the advantages are not obvious in the case of variable speed. This paper proposes a fault diagnosis algorithm in the case of variable speed.
Given the above problems, this paper proposes time-frequency compression fusion (TFCF) and residual time-frequency mixed attention network (RTFANet). Firstly, two time-frequency images obtained by TMSST and MSST are fused to transform the vibration signals into dual-channel time-frequency images. Then, the attention mechanism is introduced from three aspects of channel, time, and frequency combined with the residual connection. The model can selectively focus on essential time-frequency information, avoid information overload, and extract the practical features under the framework of the convolutional neural network to solve the problem of the weak generalization ability of the model.